Vector Calculus, 4/e (IE-Paperback)

Susan Jane Colley

  • 出版商: Prentice Hall
  • 出版日期: 2011-10-01
  • 售價: $1,250
  • 貴賓價: 9.8$1,225
  • 語言: 英文
  • 頁數: 624
  • 裝訂: Paperback
  • ISBN: 032181875X
  • ISBN-13: 9780321818751
  • 相關分類: 微積分 Calculus

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<內容簡介>

1. Vectors

  • 1.1 Vectors in Two and Three Dimensions
  • 1.2 More About Vectors
  • 1.3 The Dot Product
  • 1.4 The Cross Product
  • 1.5 Equations for Planes; Distance Problems
  • 1.6 Some n-dimensional Geometry
  • 1.7 New Coordinate Systems

2. Differentiation in Several Variables

  • 2.1 Functions of Several Variables;Graphing Surfaces
  • 2.2 Limits
  • 2.3 The Derivative
  • 2.4 Properties; Higher-order Partial Derivatives
  • 2.5 The Chain Rule
  • 2.6 Directional Derivatives and the Gradient
  • 2.7 Newton's Method (optional)

3. Vector-Valued Functions

  • 3.1 Parametrized Curves and Kepler's Laws
  • 3.2 Arclength and Differential Geometry
  • 3.3 Vector Fields: An Introduction
  • 3.4 Gradient, Divergence, Curl, and the Del Operator

4. Maxima and Minima in Several Variables

  • 4.1 Differentials and Taylor's Theorem
  • 4.2 Extrema of Functions
  • 4.3 Lagrange Multipliers
  • 4.4 Some Applications of Extrema

5. Multiple Integration

  • 5.1 Introduction: Areas and Volumes
  • 5.2 Double Integrals
  • 5.3 Changing the Order of Integration
  • 5.4 Triple Integrals
  • 5.5 Change of Variables
  • 5.6 Applications of Integration
  • 5.7 Numerical Approximations of Multiple Integrals (optional)

6. Line Integrals

  • 6.1 Scalar and Vector Line Integrals
  • 6.2 Green's Theorem
  • 6.3 Conservative Vector Fields

7. Surface Integrals and Vector Analysis

  • 7.1 Parametrized Surfaces
  • 7.2 Surface Integrals
  • 7.3 Stokes's and Gauss's Theorems
  • 7.4 Further Vector Analysis; Maxwell's Equations

8. Vector Analysis in Higher Dimensions

  • 8.1 An Introduction to Differential Forms
  • 8.2 Manifolds and Integrals of k-forms
  • 8.3 The Generalized Stokes's Theorem

Suggestions for Further Reading

Answers to Selected Exercises

Index